Parahemif
Tempering out the rastma, 243/242, leads to temperaments which divide the fifth in half and use it as an 11/9 neutral third. Temperaments not listed include jove, jovis, jofur, jovial, spectacle, mirwomo, mandos, mirage and hagrid.

Parahemif

Commas: 243/242, 896/891

Map: [<1 1 0 -1 2|, <0 2 0 13 5|, <0 0 1 0 0|]
EDOs: 17, 24, 41, 58, 99f, 123
10^5 * Badness: 134.547

13-limit

Commas: 144/143, 243/242, 364/363

Map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|, <0 0 1 0 0 0|]
EDOs: 17, 24, 34d, 41, 58, 99ef, 157ef
10^5 * Badness: 119.366